Preliminary data analyses indicate that you can reasonably use a t-test to conduct each of the hypothesis tests required in ExercisesApparel and Services. According to the document Consumer Expenditures, a publication of the Bureau of Labor Statistics, the average consumer unit spent $1736 on apparel and services in 2012. That same year, 25 consumer units in the Northeast had the following annual expenditures, in dollars, on apparel and services.1279145720201682127322232233219216111734268820292166186024441844176522671522201219901751211322021712At the 5% significance level, do the data provide sufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1736? (Note: The sample mean and sample standard deviation of the data are $1922.76 and $350.90, respectively.)

From the given information, the sample size 25.Using EXCEL function, “AVERAGE(A1:A25)”, the mean is…

Answered: Preliminary data analyses indicate that…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Preliminary data analyses indicate that you can reasonably use a t-test to conduct each of the hypothesis tests required in Exercises

Apparel and Services. According to the document Consumer Expenditures, a publication of the Bureau of Labor Statistics, the average consumer unit spent $1736 on apparel and services in 2012. That same year, 25 consumer units in the Northeast had the following annual expenditures, in dollars, on apparel and services.

1279	1457	2020	1682	1273
2223	2233	2192	1611	1734
2688	2029	2166	1860	2444
1844	1765	2267	1522	2012
1990	1751	2113	2202	1712

At the 5% significance level, do the data provide sufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1736? (Note: The sample mean and sample standard deviation of the data are $1922.76 and $350.90, respectively.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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